Can you run the pool without the skimmer just using the main drain for circulation if you think you have a leak in the underground pipe from the skimmer to the pump?

Sure you can. You'll need to use a net to clean the junk off the top often so it doesn't sink and cause stains or clog up the main drain.

You can however it would be a good Idea to repair or replace the existing skimmer with a different method of skimming say a suction side floating skimmer as there are many materials that float to the top of a swimming pool that may be hazardous to health RB